Analytic continued fraction theory for a class of confinement potentials

A general class of confinement potentials is studied in Schroedinger theory using the analytic theory of continued fractions. An infinite continued fraction representation is constructed for the Green's function and its convergence, its analytic properties in the major coupling constant and its relation to the perturbation series are studied. The existence of normalizable confined state eigensolutions with equally spaced energy levels is proved if certain constraints on the coupling constants of the theory are satisfied: it is also shown that under a separate set of constraints neither bound nor confined states exist. (Auth.)